Opaque media such as paint, milk, foam, emulsions, colloidal suspensions and human tissue do not strongly absorb visible light, while being optically turbid. This turbidity is a result of a very short scattering length characteristic of photons traveling within these media. The light does not travel in straight lines through such substances, and instead “diffuses” in a manner similar to heat flow. In other words, photons are multiply scattered within these media until they are either absorbed, or they exit the boundaries of the medium.
Recently, there has been a significant interest in the use of optical radiation for imaging within the highly scattering media, such as a biological tissue. Photons can travel within a highly scattering medium along a distribution of paths, of which very few are straight. Thus, the direction of the light into a highly scattering medium and a subsequent direction of the diffuse light emitted from the medium provides certain information regarding local variations in the scattering and absorption coefficients. Such information can identify, for example, a breast or brain tumor, bleeding in the brain, or aneurysm. Furthermore, multiple wavelengths can be used to spectroscopically determine local tissue concentrations of oxy-hemoglobin (HbO) and deoxy-hemoglobin (Hb) in tissue, which can vary in response to some stimulus, e.g., a drug. For a general description of such applications, see, e.g., A. Yodh et al., Physics Today, 34-40, March 1995.
If the spatially varying optical properties of a highly scattering medium are known, photon propagation within the medium can be calculated numerically. This numerical calculation is simplified when the scattering is much larger than the absorption, in which case photon propagation can be approximated as a diffusion process. This condition is typically satisfied in a biological tissue in the spectral range of about 700 to 900 nm. The numerical calculation gives the distribution of light inside a highly scattering medium, and is usually referred to as the “forward calculation.” For a medium being imaged, however, the “inverse calculation” should be solved, e.g., by deducing the distribution of optical properties within the medium from the diffuse light measurements. Numerical techniques for performing the inverse calculation include singular value decomposition (SVD), simultaneous iterative reconstruction technique (SIRT), K-space diffraction tomography, and a use of an extended Kaman filter. For a general review of techniques for the forward and inverse calculations, see, e.g., S. R. Arridge, Inverse Problems, 15:841, 1999.
In the art of diffuse optical tomography (“DOT”), multiple sources sequentially direct the light into a highly scattering medium (e.g., tissue), at spatially separated locations. For each such source, multiple detectors on the tissue measure the diffuse light emitted from the sample at spatially separated locations. The detectors may further obtain one or more parameters of the diffuse light emitted, e.g., fluence, and then utilize those parameters as input in the inverse calculation. However, the measurements can include various errors caused by, for example, source and detector coupling to the tissue, source and detector positional uncertainties, fluctuations in the source power, and variations in the detector gain.
to minimize these uncertainties, DOT systems are typically calibrated with initial measurements for a known sample, and the calibration is used to correct the subsequent measurements for imaging an unknown sample. Unfortunately, errors can vary from a measurement to another measurement because of, e.g., the movement or perspiration of a patient or the movement of an optical fiber that forms part of a source or detector. Thus, the results of an inverse calculation can include experimental systematic errors caused by measurement variations that are independent of the medium's properties of interest. The experimental systematic errors can also limit absolute spectroscopic measurements of the optical properties at a particular spatial location, i.e., absolute, rather than relative, values of absorption and scattering.
International Application No. WO 01/19241 describes a calibration methodology for the diffuse optical measurements that corrects the transmittance measurements between a source and a detector for factors unrelated to sample properties. The calibration methodology is based on the same set of transmittance measurements that are subsequently corrected by the calibration, and then are used in imaging and/or spectroscopy applications. This calibration method involves a forward calculation for each of multiple source-detector pairs based on an approximate model of the sample, and a minimization of an expression that depends on the forward calculations and the transmittance measurements to determine self-consistent coupling coefficients for every source-detector pair. Once the coupling coefficients are determined, they are used to correct the transmittance measurements. An inverse calculation is performed on the corrected sample measurements to determine spatial variations in the optical properties of the sample.